A simple test for spacetime symmetry. (30th January 2015)

• Record Type: Journal Article
• Authors: Houri, Tsuyoshi; Yasui, Yukinori
• Is Part Of: Classical and quantum gravity. Volume 32:Number 5(2015:Mar.)
• Publication Date: 2015-01-30
• Subjects: Killing vector field -- Killing–Yano tensor -- overdermined PDE system -- spacetime symmetry; 02.40.Hw -- 02.40.Ky -- 04.20.-q -- 4.20.Cv; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/0264-9381/32/5/055002
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: This paper presents a simple method for investigating spacetime symmetry for a given metric. The method makes use of the curvature conditions that are obtained from the Killing equations. We use the solutions of the curvature conditions to compute an upper bound on the number of Killing vector fields, as well as Killing–Yano (KY) tensors and closed conformal KY tensors. We also use them in the integration of the Killing equations. By means of the method, we thoroughly investigate KY symmetry of type D vacuum solutions such as the Kerr metric in four dimensions. The method is also applied to a large variety of physical metrics in four and five dimensions.